Unbiased Primordial Gravitational Wave Inference from the CMB with SMICA

TL;DR

This paper demonstrates that unbiased inference of primordial B-mode power, quantified by the tensor-to-scalar ratio $r$, is achievable with SMICA on small, ground-based sky patches even under complex foregrounds. By modeling the sky as a sum of independent components with a flexible, blind mixing matrix and performing likelihood-based parameter fitting via NUTS in a JAX framework, the authors show that using an adequate number of foreground components recovers unbiased $r$ values, albeit with increased uncertainty. A key finding is that adding components to capture residual foreground power is essential for removing bias in higher-foreground scenarios, and a noise-whitened SVD diagnostic can inform how many components are needed; however, the goodness-of-fit $\chi^2/n_\text{dof}$ is not a reliable indicator of $r$-bias. Overall, the method provides a robust framework for foreground marginalization in CMB-S4-like analyses, with implications for current experiments as well.

Abstract

The detection of primordial gravitational waves in Cosmic Microwave Background B-mode polarization observations requires accurate and robust subtraction of astrophysical contamination. We show, using a blind Spectral Matching Independent Component Analysis, that it is possible to infer unbiased estimates of the primordial B-mode signal from ground-based observations of a small patch of sky even for highly complex foreground contamination. This work, originally performed in the context of configuration studies for a future CMB-S4 observatory, is highly relevant for the analysis of observations by the current generation of CMB experiments.

Figures (8)

• Figure 1: Sky patch (left) with binary outline traced in black, centered at (RA = $10^\circ$, dec = $-45^\circ$). The apodization yields $f_\text{sky}=2.5\%$ as calculated with Eq. \ref{['eqn:fsky']}. The sky map is polarized intensity of the PySM3 high-complexity foregrounds at 270 GHz. Plot of beam deconvolved noise curves (right) from noise levels in Table \ref{['tab:S4specs']} for both experimental configurations. Overlaid are the theoretical CMB signals -- lensing signal (black) and primordial $B$-mode signal (red). The $\ell$-range used in the analysis is bounded by the dotted vertical black lines.
• Figure 2: Maps of total simulated $B$-mode observations in three of the frequency channels, illustrating the contributions at low frequency dominated by synchrotron (left), at the highest frequency dominated by dust (right), and in a CMB channel (middle). The CMB signal is assumed to be delensed with $A_{\rm lens}=0.08$, and in this example includes tensor modes with $r=3\times10^{-3}$.
• Figure 3: Flowchart describing our SMICA pipeline. The boxes indicate the main parts of the SMICA pipeline. The covariance matrices are computed as in Eq. \ref{['eqn:covmat']} and are the main inputs to the pipeline.
• Figure 4: SMICA posterior of $r$ in the case of low-complexity foregrounds for both $r=0$ (left) and $r=3\times10^{-3}$ (right), with measurement values are given in Tables \ref{['tab:r=0']}, \ref{['tab:r=0.003']}. Both experimental configurations are shown, and only the $n_\text{FG}=2$ model was used. The theory value of $r$ used for the input maps is marked by the vertical gray line.
• Figure 5: SMICA posterior of $r$ in the case of medium-complexity foregrounds for both $r=0$ (left) and $r=3\times10^{-3}$ (right), with measurement values are given in Tables \ref{['tab:r=0']}, \ref{['tab:r=0.003']}. Both experimental configurations are shown, with the number of foreground components ($n_\text{FG}$) used in the SMICA model marked by different colors. The theory value of $r$ used for the input maps is marked by the vertical gray line.